Dynamic Analysis of Beddington–DeAngelis Predator-Prey System with Nonlinear Impulse Feedback Control
In this paper, a predator-prey system with pesticide dose-responded nonlinear pulse of Beddington–DeAngelis functional response is established. First, we construct the Poincaré map of the impulsive semidynamic system and discuss its main properties including the monotonicity, differentiability, fixe...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/5308014 |
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| _version_ | 1832551576226496512 |
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| author | Dezhao Li Huidong Cheng Yu Liu |
| author_facet | Dezhao Li Huidong Cheng Yu Liu |
| author_sort | Dezhao Li |
| collection | DOAJ |
| description | In this paper, a predator-prey system with pesticide dose-responded nonlinear pulse of Beddington–DeAngelis functional response is established. First, we construct the Poincaré map of the impulsive semidynamic system and discuss its main properties including the monotonicity, differentiability, fixed point, and asymptote. Second, we address the existence and globally asymptotic stability of the order-1 periodic solution and the sufficient conditions for the existence of the order-k(k ≥ 2) periodic solution. Thirdly, we give the threshold conditions for the existence and stability of boundary periodic solutions and present the parameter analysis. The results show that the pesticide dosage increases with the extension of the control period and decreases with the increase of the threshold. Besides, the state pulse feedback control can manage the pest population at a certain level and avoid excessive application of pesticides. |
| format | Article |
| id | doaj-art-02bb5dce473a4520b35c36afa4eb34e9 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-02bb5dce473a4520b35c36afa4eb34e92025-02-03T06:01:00ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/53080145308014Dynamic Analysis of Beddington–DeAngelis Predator-Prey System with Nonlinear Impulse Feedback ControlDezhao Li0Huidong Cheng1Yu Liu2College of Mathematics and System Sciences, Shandong University of Science and Technology, Qingdao 266590, Shandong, ChinaCollege of Mathematics and System Sciences, Shandong University of Science and Technology, Qingdao 266590, Shandong, ChinaCollege of Foreign Languages, Shandong University of Science and Technology, Qingdao 266590, Shandong, ChinaIn this paper, a predator-prey system with pesticide dose-responded nonlinear pulse of Beddington–DeAngelis functional response is established. First, we construct the Poincaré map of the impulsive semidynamic system and discuss its main properties including the monotonicity, differentiability, fixed point, and asymptote. Second, we address the existence and globally asymptotic stability of the order-1 periodic solution and the sufficient conditions for the existence of the order-k(k ≥ 2) periodic solution. Thirdly, we give the threshold conditions for the existence and stability of boundary periodic solutions and present the parameter analysis. The results show that the pesticide dosage increases with the extension of the control period and decreases with the increase of the threshold. Besides, the state pulse feedback control can manage the pest population at a certain level and avoid excessive application of pesticides.http://dx.doi.org/10.1155/2019/5308014 |
| spellingShingle | Dezhao Li Huidong Cheng Yu Liu Dynamic Analysis of Beddington–DeAngelis Predator-Prey System with Nonlinear Impulse Feedback Control Complexity |
| title | Dynamic Analysis of Beddington–DeAngelis Predator-Prey System with Nonlinear Impulse Feedback Control |
| title_full | Dynamic Analysis of Beddington–DeAngelis Predator-Prey System with Nonlinear Impulse Feedback Control |
| title_fullStr | Dynamic Analysis of Beddington–DeAngelis Predator-Prey System with Nonlinear Impulse Feedback Control |
| title_full_unstemmed | Dynamic Analysis of Beddington–DeAngelis Predator-Prey System with Nonlinear Impulse Feedback Control |
| title_short | Dynamic Analysis of Beddington–DeAngelis Predator-Prey System with Nonlinear Impulse Feedback Control |
| title_sort | dynamic analysis of beddington deangelis predator prey system with nonlinear impulse feedback control |
| url | http://dx.doi.org/10.1155/2019/5308014 |
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